So who is this app for?
Eventually, Microsoft would hope the answer to that question would be "everyone," but right now I'm not so sure. Apps like Spotify and Slacker Radio let you browse genres, offer collections of music to listen to, and you can check out featured artists to find new music.
While Xbox Music doesn't have any of these music discovery features, I still think if you own an Xbox that's hooked up to your entertainment system, the service will be worth the price to have your music collection and playlists wherever you are. So, basically, if you don't own an Xbox, don't bother with the service until more features are added.
Xbox Music feels more like a "good start" than what the finished product will eventually be. On the positive side, the menus are smooth and responsive, and songs start playing almost immediately. But requiring the Xbox Music Pass means that you cannot use the app at all without signing up with a credit card (though you do get 30 days free). With Spotify or Slacker, you can at least listen to radio stations for free, but things like music on demand are what's behind the subscription wall.
Still, Xbox Music will be useful for access to music on all your devices including your home entertainment center (with an Xbox). With the addition of music discovery features and ironing out the rough edges, Xbox music could be a major player in streaming-music software. But for right now, only those who have an XBox connected to a home entertainment system should pick this app over other more-feature-rich services.